 
Summary: Points and Combinatorics
Oswin Aichholzer, Franz Aurenhammer, Hannes Krasser
Institute for Theoretical Computer Science
Graz University of Technology
Graz, Austria
email: foaich,auren,hkrasserg@igi.tugraz.ac.at
Which point sets exist, anyway?
This intuitive question sketches the topic of the article
at hands. Its relevance is apparent: a conguration of
n points is the underlying structure for countless prob
lems in computational and combinatorial geometry.
In fact, a point set in the Euclidean plane is among
the simplest geometric objects that lead to nontrivial
questions { in a geometrical, combinatorial, and algo
rithmic sense. Not surprisingly, most basic data struc
tures in computational geometry have rst been devel
oped for point sets, and have been later generalized to
more general objects, like line segments, circles, poly
gons, etc. Examples include geometric search trees,
convex hulls, Voronoi diagrams (an accompaning ar
